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June 2010 Existence of Standing Waves for Coupled Nonlinear Schrödinger Equations
Norihisa IKOMA
Tokyo J. Math. 33(1): 89-116 (June 2010). DOI: 10.3836/tjm/1279719580

Abstract

In this paper we study the existence of standing waves for coupled nonlinear Schrödinger equations. The interaction between equations plays an important role in our study. When the interaction is strong, the least energy solution is a solution whose both components are positive. When the interaction is weak, the least energy solution is a semitrivial solution, namely a solution of a form $(u_1,0)$ or $(0,u_2)$. Moreover, minimizing method on the Nehari type manifold with codimension 2 gives us a positive solution when the interaction is weak.

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Norihisa IKOMA. "Existence of Standing Waves for Coupled Nonlinear Schrödinger Equations." Tokyo J. Math. 33 (1) 89 - 116, June 2010. https://doi.org/10.3836/tjm/1279719580

Information

Published: June 2010
First available in Project Euclid: 21 July 2010

zbMATH: 1198.35257
MathSciNet: MR2682883
Digital Object Identifier: 10.3836/tjm/1279719580

Rights: Copyright © 2010 Publication Committee for the Tokyo Journal of Mathematics

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Vol.33 • No. 1 • June 2010
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